Math - Vectors

Relative to an origin O, the position vectors of points A and B are given by
OA = 3pi + 4j + p^2k, and
OB = -pi + -1j + p^2k

Find the values of p for which angle AOB is 90°

So here's my work so far:
If angle = 90° then OA.OB = 0
OA.OB = p^4 - 3p^2 - 4
p^4 - 3p^2 - 4 = 0

Let x = p^2
x^2 - 3x - 4 = 0
x = 4 or -1

What do I do now?

Thanks for the help!

  1. 0
  2. 4
asked by Autumn
  1. remember you let y = p^2
    so p^2 = 4 ----> p = ± 2
    or
    p^2 = -1 , which has no real solution.

    so p = ± 2

    1. 0
    posted by Reiny
  2. Wait, but doesn't the question say 'values'?

    1. 0
    posted by Autumn
  3. Oh wait, just realized how dumb that was! Had a brain fart, thanks for clearing things up!

    1. 0
    posted by Autumn

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths Vector Helpppp

    The points A and B have position vectors, relative to the origin O, given by −−→OA = i+2j+3k and −−→OB = 2i+j+3k. The line l has vector equation r = (1−2t)i+ (5+t)j+ (2−t)k. (i) Show that l does not intersect the
  2. Physics

    1. Consider the two vectors P and Q. The definition of P is P = 􀀃i × (􀀃i × 􀀃j). The definition of Q is Q = (􀀃i × 􀀃i) × 􀀃j . a. The magnitude of P is equal to the magnitude of Q. b. The magnitude of P is
  3. Maths - Vectors

    The position vectors a,b,c of the points A,B,C relative to the origin O are ai, bj and ck respectively.Find: 1) a vector equation for the line l throught O which is normal to the plane ABC. 2) a vector equation of the plane ABC
  4. Calculus

    Sketch the vector field F⃗ (r⃗ )=2r⃗ in the plane, where r⃗ =⟨x,y⟩. Select all that apply. A.All the vectors point away from the origin. B. The vectors increase in length as you move away from the origin. C. All the
  5. AP Physics

    At time t=0, a 2kg particle has position vector r=(5.0m)i+(-8.0m)j relative to the origin. Its velocity just then is given by v=(-5.0t^2m/s)i. For the following answers, use t for the time. A) About the origin and for t>0, what is
  6. phy

    A boat can travel 2.60 m/s in still water.If the boat points its prow directly across a stream whose current is 1.10 m/s, what is the velocity (magnitude and direction) of the boat relative to the shore? What will be the position
  7. physics

    two inertial frame s and s' have their axes paralell and pasitions of origin o' of s' relative to origin to s is given by ro=i+j+3k.what is the magnitude of position vector of a point p in s' if the co-ordinates p in s is(2,3,4)
  8. Math

    The position vectors for points P and Q are 4 I + 3 j + 6 j + 6 k respectively. Express vector PQ in terms of unit vectors I, j and k. Hence find the length of PQ, in simplified surd form.
  9. math

    the position vectors of A and B relative to the origin are a and b repsectively The point P is on OA such that PA=2PA So my question is if B is the top of the triangle and O represent the left corner of the triangle and A the
  10. 12th grade

    prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a

More Similar Questions